Title: Resolution Versus Error for Computational Electron Microscopy

Abstract

Images that are collected via scanning transmission electron microscopy (STEM) can be undersampled to avoid damage to the specimen while maintaining resolution [1, 2]. We have used BPFA to impute missing data and reduce noise [3]. The reconstruction is typically evaluated using the peak signal-to-noise ratio (PSNR). This measure is too conservative for STEM images and we propose that the Fourier ring correlation (FRC) is used instead to evaluate the reconstruction. We are not concerned with exact reconstruction of the truth image, and therefore PSNR is a conservative estimation of the quality of the reconstruction. Instead, we are concerned with the visual resolution of the image and whether atoms can be distinguished. We have evaluated the reconstruction of a simulated STEM image using the FRC and compared the results with the PSNR measurements. The FRC captures the resolution of the image and is not affected by a large MSE if the atom peaks are still distinguishable. The noisy and reconstructed images are shown in Figure 1. The simulated STEM image was sampled at 100%, 80%, 40%, and 20% of the original pixels to simulate an undersampled scan. The reconstruction was done using BPFA with a patch size of 10 xmore » 10 and no overlapping patches. Not having overlapping patches produces inferior results but they are still acceptable. The dictionary size is 64 and 30 iterations were completed during each reconstruction. The 100% image was denoised instead of reconstructed. Poisson noise was applied to the simulated image with λ values of 500, 50, and 5 to simulate lower imaging dose. The original simulated STEM image was also included in our calculations and was generated using a dose of 1000. The simulated STEM image is 100 by 100 pixels and has essentially no high frequency components. The image reconstruction tends to smooth the data, also resulting in no high frequency components. This causes the FRC of the two images to be large at higher resolutions and may be misleading. For this reason, the BPFA has no overlap to avoid excessive smoothing. Moreover, the resolution of the simulated image is approximately 9.2 (1/nm), so we only look that far in the frequency domain when performing FRC. If the FRC curve does not crossover the threshold, a resolution value of 9.2 is used. We emphasize that our reported results are conservative. The FRC and PSNR values using the ground truth and the reconstructed images are shown in Tables 1 and 2. The left side show the metrics without using BPFA (missing pixels) and the right side show the metrics after using BPFA. When we did not use BPFA, the Fourier transform was estimated [4]. Some threshold curves have been studied [5], but they are derived for additive noise models. Since we have a Poisson noise model, we have used the more conservative threshold of 0.5 for our calculations. Ten images were used to construct each cell of tables in the form of the mean of the metric plus or minus its standard deviation. As expected, the PSNR dies off much quicker than the FRC values for the same image. For the 100% and 80% sampled versions of the truth image, the resolution only dies off when the dose is 5. However, the PSNR dies off rapidly as the dose is reduced. For the 1000, 500, and 50 dose images, the FRC is the maximum, or close, until we undersample at 20%. The PSNR for these values tapers down as we get into the bottom right hand corner of the table, even though the resolution remains high. Overall, we find that undersampled images can be reconstructed to acceptable resolution even when the dose per pixel is also reduced[6]. References: [1]A Stevens, H Yang, L Carin et al. Microscopy 63(1), (2014), pp. 41. [2]A Stevens, L Kovarik, P Abellan et al. Advanced Structural and Chemical Imaging 1(1), (2015), pp. 1. [3]M Zhou, H Chen, J Paisley et al. Image Processing, IEEE Transactions on 21(1), (2012), pp. 130. [4]V. Y. Liepin’sh. Automatic control and computer sciences 30(3), (1996), pp. 20.« less

@article{osti_1379438,
title = {Resolution Versus Error for Computational Electron Microscopy},
author = {Luzi, Lorenzo and Stevens, Andrew and Yang, Hao and Browning, Nigel D.},
abstractNote = {Images that are collected via scanning transmission electron microscopy (STEM) can be undersampled to avoid damage to the specimen while maintaining resolution [1, 2]. We have used BPFA to impute missing data and reduce noise [3]. The reconstruction is typically evaluated using the peak signal-to-noise ratio (PSNR). This measure is too conservative for STEM images and we propose that the Fourier ring correlation (FRC) is used instead to evaluate the reconstruction. We are not concerned with exact reconstruction of the truth image, and therefore PSNR is a conservative estimation of the quality of the reconstruction. Instead, we are concerned with the visual resolution of the image and whether atoms can be distinguished. We have evaluated the reconstruction of a simulated STEM image using the FRC and compared the results with the PSNR measurements. The FRC captures the resolution of the image and is not affected by a large MSE if the atom peaks are still distinguishable. The noisy and reconstructed images are shown in Figure 1. The simulated STEM image was sampled at 100%, 80%, 40%, and 20% of the original pixels to simulate an undersampled scan. The reconstruction was done using BPFA with a patch size of 10 x 10 and no overlapping patches. Not having overlapping patches produces inferior results but they are still acceptable. The dictionary size is 64 and 30 iterations were completed during each reconstruction. The 100% image was denoised instead of reconstructed. Poisson noise was applied to the simulated image with λ values of 500, 50, and 5 to simulate lower imaging dose. The original simulated STEM image was also included in our calculations and was generated using a dose of 1000. The simulated STEM image is 100 by 100 pixels and has essentially no high frequency components. The image reconstruction tends to smooth the data, also resulting in no high frequency components. This causes the FRC of the two images to be large at higher resolutions and may be misleading. For this reason, the BPFA has no overlap to avoid excessive smoothing. Moreover, the resolution of the simulated image is approximately 9.2 (1/nm), so we only look that far in the frequency domain when performing FRC. If the FRC curve does not crossover the threshold, a resolution value of 9.2 is used. We emphasize that our reported results are conservative. The FRC and PSNR values using the ground truth and the reconstructed images are shown in Tables 1 and 2. The left side show the metrics without using BPFA (missing pixels) and the right side show the metrics after using BPFA. When we did not use BPFA, the Fourier transform was estimated [4]. Some threshold curves have been studied [5], but they are derived for additive noise models. Since we have a Poisson noise model, we have used the more conservative threshold of 0.5 for our calculations. Ten images were used to construct each cell of tables in the form of the mean of the metric plus or minus its standard deviation. As expected, the PSNR dies off much quicker than the FRC values for the same image. For the 100% and 80% sampled versions of the truth image, the resolution only dies off when the dose is 5. However, the PSNR dies off rapidly as the dose is reduced. For the 1000, 500, and 50 dose images, the FRC is the maximum, or close, until we undersample at 20%. The PSNR for these values tapers down as we get into the bottom right hand corner of the table, even though the resolution remains high. Overall, we find that undersampled images can be reconstructed to acceptable resolution even when the dose per pixel is also reduced[6]. References: [1]A Stevens, H Yang, L Carin et al. Microscopy 63(1), (2014), pp. 41. [2]A Stevens, L Kovarik, P Abellan et al. Advanced Structural and Chemical Imaging 1(1), (2015), pp. 1. [3]M Zhou, H Chen, J Paisley et al. Image Processing, IEEE Transactions on 21(1), (2012), pp. 130. [4]V. Y. Liepin’sh. Automatic control and computer sciences 30(3), (1996), pp. 20.},
doi = {10.1017/S143192761700112X},
journal = {Microscopy and Microanalysis},
number = S1,
volume = 23,
place = {United States},
year = 2017,
month = 7
}

A theoretical and experimental investigation of contrast and resolution versus specimen thickness in scanning transmission electron microscopy at low energy is reported. Due to absence of postspecimen imaging lenses it is possible to have images with a resolution defined by the probe size using very wide collection angles and independent of the energy loss of the transmitted electrons. The fundamental limitation in observable specimen thickness is represented by the signal to noise ratio, i.e., the intensity of the beam current. The investigated specimens are semiconductor multilayers and Sb precipitates in a Si implanted specimen. The observations of layers crossing themore » whole specimens parallel to the electron beam point out that only a small portion of them, the one close to the surface, causes the image contrast, while the portion below, where the probe diameter, as a consequence of the broadening, is larger than the layer itself, reduces the contrast. A similarity with recent results, achieved in scanning transmission electron microscopy at high energy, where the layers are represented by atomic columns, is pointed out. The image contrast depends on the angular distribution of the transmitted electrons, and for thick specimens it is always of bright field type, independent of the collection angle of the transmitted electrons. The observation of Sb precipitates, distributed along the specimen thickness, evidences the role of beam broadening on the resolution and contrast.« less

Batteries based on Mg metal anode can promise much higher specific volumetric capacity and energy density compared to Li-ion systems and are, at the same time, safer and more cost-effective. While previous experimental reports have claimed reversible Mg intercalation into beyond Chevrel phase cathodes, they provide limited evidence of true Mg intercalation other than electrochemical data. Transmission electron microscopy techniques provide unique capabilities to directly image Mg intercalation and quantify the redox reaction within the cathode material. Here, we present a systematic study of Mg insertion into orthorhombic V 2O 5, combining aberration-corrected scanning transmission electron microscopy (STEM) imaging, electronmore » energy-loss spectroscopy (EELS), and energy-dispersive X-ray spectroscopy (EDX) analysis. We compare the results from an electrochemically cycled V 2O 5 cathode in a prospective full cell with Mg metal anode with a chemically synthesized MgV 2O 5 sample. Results suggest that the electrochemically cycled orthorhombic V 2O 5 cathode shows a local formation of the theoretically predicted ϵ-Mg0.5V2O5 phase; however, the intercalation levels of Mg are lower than predicted. Lastly, this phase is different from the chemically synthesized sample, which is found to represent the δ-MgV 2O 5 phase.« less

Abstract A long-standing goal of electron microscopy has been the high-resolution characterization of specimens in their native environment. However, electron optics require high vacuum to maintain an unscattered and focused probe, a challenge for specimens requiring atmospheric or liquid environments. Here, we use an electron-transparent window at the base of a scanning electron microscope’s objective lens to separate column vacuum from the specimen, enabling imaging under ambient conditions, without a specimen vacuum chamber. We demonstrate in-air imaging of specimens at nanoscale resolution using backscattered scanning electron microscopy (airSEM) and scanning transmission electron microscopy. We explore resolution and contrast using Montemore » Carlo simulations and analytical models. We find that nanometer-scale resolution can be obtained at gas path lengths up to 400μm, although contrast drops with increasing gas path length. As the electron-transparent window scatters considerably more than gas at our operating conditions, we observe that the densities and thicknesses of the electron-transparent window are the dominant limiting factors for image contrast at lower operating voltages. By enabling a variety of detector configurations, the airSEM is applicable to a wide range of environmental experiments including the imaging of hydrated biological specimens andin situchemical and electrochemical processes.« less

Structural properties of the clean Si(001) surface obtained as a result of low-temperature (470-650 Degree-Sign C) pre-growth annealings of silicon wafers in a molecular-beam epitaxy chamber have been investigated. To decrease the cleaning temperature, a silicon surface was hydrogenated in the process of a preliminary chemical treatment in HF and NH{sub 4}F aqueous solutions. It has been shown that smooth surfaces composed of wide terraces separated by monoatomic steps can be obtained by dehydrogenation at the temperatures Greater-Than-Or-Equivalent-To 600 Degree-Sign C, whereas clean surfaces obtained at the temperatures <600 Degree-Sign C are rough. It has been found that there existsmore » a dependence of structural properties of clean surfaces on the temperature of hydrogen thermal desorption and the process of the preliminary chemical treatment. The frequency of detachment/attachment of Si dimers from/to the steps and effect of the Ehrlich-Schwoebel barrier on ad-dimer migration across steps have been found to be the most probable factors determining a degree of the resultant surface roughness.« less

Bioinert materials (e.g., alumina implants) and bioactive ceramics (e.g., calcium phosphate ceramics, glass-ceramics) are now extensively used in dentistry. However, the physico-chemical interactions at the interfaces between the implant and the host bone are poorly understood. The purpose of this study was to define the interactions at these interfaces using a combination of analytical techniques: light microscopy, scanning and transmission electron microscopy, electron probe microanalysis, X-ray microradiography, X-ray diffraction, and infrared spectroscopy. Bioinert (pure titanium) and bioactive materials (hydroxyapatite, beta-tricalcium phosphate and biphasic calcium phosphate) were implanted in dogs, and the implants, recovered after various periods of implantation, were analyzed.more » The results demonstrated the following: the bioactive materials interact with the biological fluid and the living tissues in a specific manner. This process includes biodissolution/biodegradation, apatite crystal precipitation, and bone formation on the implant surface at the expense of the material. The results are discussed according to the limitations of the analytical techniques used. The medical and chemical word coalescence is suggested to describe the specific interactions of bioactive materials and interaction for the phenomenon of physical contact of the bioinert materials with the host bone.« less